OKAN UNIVERSITY FACULTY OF ENGINEERING AND ARCHITECTURE 1 EEE 403 DIGITAL SIGNAL PROCESSING (DSP) 01 INTRODUCTION FALL 2012 Yrd. Doç. Dr. Didem Kıvanç Türeli didem.kivanc@okan.edu.tr EE 403: Digital Signal Processing 2 Instructor: Didem Kıvanç Türeli didem.kivanc@okan.edu.tr didemk@ieee.org Phone:(216) 677-1630 Ext. 1936 Office: D328 Class: Monday 9:00-12:00 Room D303 Course website: http://personals.okan.edu.tr/didem.kivanc 1
EE 403: Digital Signal Processing 3 Textbooks Dimitris G. Manolakis, Vinay K. Ingle, Applied Digital Signal Processing: Theory and Practice, Cambridge University Press, ISBN-10: 0521110025, ISBN-13: 978-0521110020 Robert J. Schilling, Sandra L Harris, Fundamentals of Digital Signal Processing Using MATLAB, CL Engineering, 2nd Edition. ISBN-10: 084006909X, ISBN-13: 978-0840069092 Alan Oppenheim, Ronald Schafer, John Buck, Discrete-Time Signal Processing, Prentice Hall, 2nd Edition. Course Outline Time-domain analysis of discrete signals and systems, frequency-domain signal analysis: DTFT, z-transform, DFT, FFT, FIR and IIR digital filters, digital filter theory, design and implementation. Prerequisites Matlab, Simulink, Calculus I,II,III,IV, Signals and Systems EE 403 Grading Policy 4 1 Midterm 1 Final Labs + Homework + Quizzes Grading Formula: Final Grade = 0.05 Quiz + 0.25 (Homework and Labs) + 0.3 Midterm + 0.4 Final 2
Academic Dishonesty 5 Any violation of academic integrity will receive academic and possibly disciplinary sanctions. The sanctions include the possible awarding of a F grade. Cheating Copying on a test Plagiarism Acts of aiding or abetting Submitting previous work Tampering with work Altering exams Course Objectives 6 Upon completing this course, students will be able to identify applications in which digital signal processing could be used. Students will be able to design, implement, analyze and debug digital signal processing algorithms. 3
7 Course Plan Week 1. (Sep. 17 th ) Week 2. (Sep. 24 th ) LAB 1 Week 3. (Oct. 1 st ) LAB 2 Week 4. (Oct. 8 th ) LAB 3 Week 5. (Oct. 15 th ) LAB 4 Week 6. (Oct. 22 nd ) Course Outline (1/2) Introduction to Digital Signal Processing, Discrete time signals and systems (S 24 th ) Periodic Sampling and Quantization Sampling and Quantization of Analog Signals The z-transform Moving Average Filters The Discrete Time Fourier Transform and the Discrete Fourier Transform DFT of Digital Signals The Discrete Time Fourier Transform and the Discrete Fourier Transform Implementation of FFT Fast Fourier Transform Implementation of FFT LAB 5 Week 7. (Oct. 29 st ) Midterm 1 8 Course Plan Week 8. (Nov. 5 th ) LAB 6 Week 9. (Nov. 12 th ) LAB 7 Week 10. (Nov. 19 th ) LAB 8 Week 11. (Nov. 26 th ) LAB 9 Week 12. (Dec. 3 rd ) LAB 10 Week 13. (Dec. 10 th ) LAB 11 Week 14. (Dec. 17 th ) Course Outline (2/2) Finite Impulse Response Filters FIR Filter Finite Impulse Response Filters, Infinite Impulse Response Filters Signal Detection using FIR filter Infinite Impulse Response Filters Low Pass IIR Filters Transforms Filter Design using Transformations Adaptive Signal Processing Adaptive Filter Data Formats and their Effects, Quantization Digital Implementation of Controllers REVIEW 4
9 Signals What is a signal? 10 A signal is a physical variable whose value varies with time or space. 1 We are particularly l interested t in signals which h we will convert to electrical pulses using a transducer. 1 Robert J. Schilling, Sandra L Harris, Fundamentals of Digital Signal Processing Using MATLAB, CL Engineering, 2nd Edition. 5
Analog to Digital 11 12 6
Types of signals 13 Continuous va alue x Continuous time t Discrete time x x Discrete va alue t t From Analog to Digital 14 7
15 Discrete Time Systems A discrete system is a collection of hardware components or software routines that operate on a discrete time signal sequence. Example: y(n) = 2x(n) 1 DSP: the math 16 The equation y(n) = 2x(n) 1 is a difference equation. What is the frequency of the waveform? 1 0.8 0.6 0.4 0.2 0-0.2-0.4-0.6-0.8-1 1 2 3 4 5 6 7 8 9 10 10 samples 0.05 milliseconds period = 0.5 milliseconds / period period sample = 8
17 The frequency domain The Spectral Sequence Amplitude vs. magnitude 18 Not the same thing. The amplitude is a measure of how far and in which direction a variable ab differs from zero. The amplitude can be positive, negative or zero. The magnitude (or absolute value) is a measure of how far a quantity is from zero, regardless of direction. Magnitude must be positive. Power of a signal: 2 xpwr ( n ) = x ( n ) X ( m) = X( m) pwr Power is often plotted on the decibel scale. 2 9
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Linear Time Invariant Systems 21 Linear System: If x1( n) y1( n) x2( n) y2( n) then ax ( n) + bx ( n) ay ( n) + by ( n) 1 2 1 2 22 11
23 2 [ xn] ( π s) ( π s) 2 [ ] ( π ) ( π ) yn ( ) = ( ) x ( n) = sin 2 f nt = sin 2 1 nt 1 0 y ( n) = x ( n) = sin 2 1 nt sin 2 1 nt 1 1 sin cos( α β) cos( α + β) = 2 2 ( α) sin ( β) s ( π nt π nt ) ( π nt + π nt ) cos 2 1 2 1 cos 2 1 2 1 y1 ( n) = 2 2 cos( 0) cos( 4π 1 nts) 1 cos( 4π 1 nts) = = 2 2 2 2 s s s s s 24 12
Linear Time Invariant Systems 25 Time Invariant System: If xn ( ) yn ( ) then x( n+ k) y( n+ k) A time shift in the input sequence results in an equal time shift in the output sequence. A Time Invariant System 13
27 Commutative Property of Linear Time Invariant System Analyzing LTI systems 28 The LTI system s unit impulse response completely characterizes the system (i.e. tells us everything there is to know about the system). The output of the LTI system is the convolution of its unit impulse response and the input. Given an LTI system s time domain impulse response, we can find the system s frequency response by taking the discrete Fourier transform (DFT) of that impulse response. 14
29 Unit impulse response How to generate an impulse 30 Mechanical system: whack it with a hammer Electrical system: high voltage spike Acoustic system: fire a starter pistol. Digital system: 0,0,0,1,0,0,0,. 15
31 Example: moving averager 16